Bundle methods are often the algorithms of choice for nonsmooth convex optimization, especially if accuracy in the solution and reliability are a concern. We review several algorithms based on the bundle methodology that have been developed recently and that, unlike their forerunner variants, have the ability to provide exact solutions even if most of the time the available information is inaccurate. We adopt an approach that, without being exhaustive, covers several variants in the literature and allows us to consider extensions such as
- dealing with nonconvex objective functions;
- solving constrained problems; and
- exploiting underlying functional structure to achieve fast convergence.
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